And across the Nile River from Tahrir Square, Morsy supporters chanted chanted "Down with military rule" and "The square has a million martyrs."
Before Wednesday night's announcement, troops moved into key positions around the capital, closing off a bridge over the Nile and surrounding Rabaa Adawya Square, where Morsy's supporters were gathered.
Military had demanded reforms
Morsy was elected president in June 2012. But his approval ratings have plummeted as his government has failed to keep order or revive Egypt's economy. The chaos, including open sexual assaults on women in Egypt's streets, has driven away tourists and investors, while opponents say Morsy's rule was increasingly authoritarian.
Mohamed ElBaradei, the former head of the International Atomic Energy Agency and a leading opposition figure, said the plans announced Wednesday were "a correction for the way of the revolution" that drove Hosni Mubarak from office in 2011.
"The road map guarantees achieving the principal demand of the Egyptian people -- having early presidential elections through an interim period through which the constitution will be amended," he said. "So all of us build it together and agree on a democratic constitution, so we can guarantee our freedoms."
The Egyptian military dominated the country for six decades and took direct power for a year and a half after Mubarak's ouster. On Monday, after a previous demand that Morsy offer concessions to the opposition, it gave him 48 hours to order reforms.
As the hour of the ultimatum neared, Morsy offered to form an interim coalition government to oversee parliamentary elections and revise the constitution that was enacted in January.
"One of the mistakes I cannot accept -- as the president of all Egyptians -- is to side with one party over another, or to present the scene from one side only. To be fair, we need to listen to the voice of people in all squares," he said.
Shortly after the deadline, Morsy aide Essam El Haddad said in a Facebook posting that a coup was under way and warned that the generals risked bloodshed by moving against Morsy.
"In a democracy, there are simple consequences for the situation we see in Egypt: The president loses the next election or his party gets penalized in the upcoming parliamentary elections. Anything else is mob rule," he wrote.
But Naguib Abadeer, a member of the opposition Free Egyptians Party, said what was under way "is not by any means a military coup. This is a revolution."
Morsy lost his legitimacy in November, when he declared courts could not review his decrees and ousted the country's prosecutor-general, Abadeer said. And the Muslim Brotherhood "hijacked the vote of the people" by running on a religious platform, "so these were not democratic elections," he said.
Obama says U.S. reviewing aid
In Washington, President Barack Obama said the United States is "deeply concerned" by Morsy's removal and the suspension of the constitution.
Washington has supplied Egypt's military with tens of billions in support and equipment over more than 30 years, and under U.S. law, that support could be cut off after a coup -- a term his White House statement avoided.
"The United States does not support particular individuals or political parties, but we are committed to the democratic process and respect for the rule of law," Obama said.
He said he had ordered "the relevant departments and agencies" to study what American law would mean for U.S. aid and urged the generals to hand power back to an elected government 'as soon as possible."
In the wake of Morsy's ouster, U.N. Secretary-General Ban Ki-moon echoed Obama's call for an immediate return to civilian rule. He appealed for "calm, non-violence, dialogue and restraint."
Wednesday's events capped days of massive demonstrations for and against Morsy. The demonstrations were largely peaceful, but health officials said 23 people died in clashes overnight at Cairo University, Al-Ahram reported.